Linear functions and their graphs

The order of lesson themes has been deliberately changed here.
The learning objective follows a engaging task which introduces some the ideas in a student-driven context.

Investing:

• The three short videos below by Dan Mayer may prove to be an interesting starting point.
• Show one clip at a time and allow plenty of time for thinking and discussion.

• On a blog, John Scammell wrote:

"When I was a kid, I'd grind other kids' pencils down to nothing."

• Watch the first clip:

Pencil Sharpener - Act One from Dan Meyer on Vimeo.

• What mathematical question(s) does this suggest to you?
• Anything else?
  
  
• What data would you need to know to answer your question(s)?
• Is that all?

• Watch the second clip:

Pencil Sharpener - Act Two from Dan Meyer on Vimeo.

• How does the second clip change or refine your question?
• Did you get all the data you needed?

• Can you solve your problem yet?
  
  - Solve the problem!

• What else can you ask or work out?
• Why not have a play with modelling the situation with this Desmos graph page:
• 
• How else might you model the situation in Desmos? What other function would graph the problem?

• Watch the third clip - were you right?

Pencil Sharpener - Act Three from Dan Meyer on Vimeo.

• What other things in life might change in a similar way? Discuss!
• Can you make a set of video clips that present the same three-steps: 1. problem; 2. data; 3. solution?

• Learning about proportional and linear change leads to:
  • coordinate geometry: straight lines and gradients
  • conversion graphs and converting currency and units
  • speed, distance and time and other 'compound measurements' like flow rates and density
  • 
    

• A 'free gift' with this skill is that we can now also understand linear sequences (number patterns) better.

• This could help you if you want to work in...

Learning Objective:

• we are learning to recognise and use linear functions and their graphs.
• we are learning to use proportional reasoning to describe the rate of something

• our success criteria are:
  1. we can predict values using proportional and linear changes
  2. we can draw straight line graphs to show proportional and linear changes
  3. we can turn a proportional change into the relationship y = mx and recognise and imagine its graph
  4. we can turn a linear change into the relationship y = mx + c and recognise and imagine its graph
  5. we are fluent in converting between graphical, numerical and algebraic representations of proportional and linear changes

Preparing:

• Are we ready? Can you already... ?
• Let's be sure you can...
• Before you start you need to know:
• You will have a deeper understanding if you also know:

Discovering:

• Can you figure it out yourself from these examples?

• Try to predict the next one aloud or on a mini-whiteboard.
• Investigate...

Modeling:

• Here are some examples of people getting it right:
• Here are some examples of people getting it wrong in typical ways:
• Here are some more examples. Did they get it right or wrong? Explain how you know!

Discussing:

• What would this one be? Tell your learning partner. Convince them you're right.
• Explain how you know.
• How would you explain this to someone who was new to it?

Explaining:

• One way to do this is...
• Another approach might be...
• A useful shortcut is to...
• This works because...
• It doesn't work when...
• An exception is...
• Watch out for...
• A common mistake is...
• You can check your result by...
• We can prove this works by...

Practicing:

• Some straightforward examples.
• Some harder examples.
• Some mixed examples.
• Some non-examples to spot and some mixed questions with redundant, insufficient or contradictory data.
• You can demonstrate fluency by at least...

Sharing:

• A web page or wiki I have created to explain this can be found at...
• A presentation I have created and rehearsed looks like...
• A poster I have drawn or model I have made can be found...

Assessing:

• Check you've mastered this skill by...
• Show you understand by explaining...
• Prove you're an expert in... by...

Developing:

• Next we could learn...
• This leads to...
• Now try...

last edited: Dec 3, 2013 3:03 am